Concept explainers
(a)
The appropriate model to describe the system when balloon is stationary.
(a)
Answer to Problem 14.60AP
The appropriate model to describe the system is particle in equilibrium.
Explanation of Solution
The mass of the balloon is
If a system remains stationary, the sum of all forces acted on a system in all direction vertical as well as horizontal is equal to zero. This condition is also called is equilibrium condition.
Conclusion:
Therefore, appropriate model to describe the system is particle in equilibrium.
(b)
The force equation for the balloon for this model.
(b)
Answer to Problem 14.60AP
The force equation for the balloon for this model is
Explanation of Solution
In equilibrium condition, sum of all forces in vertical direction is equal to zero.
Here,
Conclusion:
Therefore, the force equation for the balloon for this model is
(c)
The mass of the string in terms of
(c)
Answer to Problem 14.60AP
The mass of the string in the terms of
Explanation of Solution
From equation (I),
The buoyant force act on the balloon is equal to the displaced volume of the air by the balloon.
Formula to calculate the buoyant force acting on the balloon is,
Here,
Formula to calculate the weight of the balloon is,
Here,
Formula to calculate the weight of the helium gas is,
Here,
Formula to calculate the weight of the string is,
Here,
Substitute
Formula to calculate the mass of the helium gas is,
Here,
Substitute
Rearrange the above expression for
Conclusion:
Therefore, the mass of the string in terms of
(d)
The mass of the string.
(d)
Answer to Problem 14.60AP
The mass of the string is
Explanation of Solution
From equation (II),
Substitute
Conclusion:
Therefore, the mass of the string is
(e)
The length
(e)
Answer to Problem 14.60AP
The length
Explanation of Solution
From equation (II),
The mass of the string of height
Substitute
Substitute
Conclusion:
Therefore, the length
Want to see more full solutions like this?
Chapter 14 Solutions
Physics for Scientists and Engineers
- In about 1657. Otto von Guericke, inventor of the air pump, evacuated a sphere made of two brass hemispheres (Fig. P9.89). Two teams of eight horses each could pull the hemispheres apart only on some trials and then with greatest difficulty, with the resulting sound likened to a cannon firing. Find the force F required to pull the thin-walled evacuated hemispheres apart in terms of R, the radius of the hemispheres, P the pressure inside the hemispheres, and atmospheric pressure P0. Figure P9.89arrow_forwardHow many cubic meters of helium are required to lift a light balloon with a 400-kg payload to a height of 8 000 m? Take Hc = 0.179 kg/m3. Assume the balloon maintains a constant volume and the density of air decreases with the altitude z according to the expression pair = 0e-z/8 000, where z is in meters and 0 = 1.20 kg/m3 is the density of air at sea level.arrow_forwardA hollow copper (Cu = 8.92 103 kg/m3) spherical shell of mass m = 0.950 kg floats on water with its entire volume below the surface. a. What is the radius of the sphere? b. What is the thickness of the shell wall?arrow_forward
- A manometer is shown in Figure P15.36. Rank the pressures at the five locations indicated from highest to lowest. Indicate equal pressures, if any. FIGURE P15.36arrow_forwardWhy is the Earths atmosphere denser near sea level than it is at a high altitude? Be sure to explain why the atmospheres density is not uniform and why the air isnt all in contact with the Earths surface.arrow_forwardHow many cubic meters of helium are required to lift a balloon with a 400-kg payload to a height of 8 000 m? Take He = 0.179 kg/m3. Assume the balloon maintains a constant volume and the density of air decreases with the altitude z according to the expression air = 0ez/8, where z is in meters and 0 = 1.20 kg/m3 is the density of air at sea level.arrow_forward
- A spherical submersible 2.00 m in radius, armed with multiple cameras, descends under water in a region of the Atlantic Ocean known for shipwrecks and finds its first shipwreck at a depth of 1.75 103 m. Seawater has density 1.03 103 kg/m3, and the air pressure at the oceans surface is 1.013 105 Pa. a. What is the absolute pressure at the depth of the shipwreck? b. What is the buoyant force on the submersible at the depth of the shipwreck?arrow_forwardA vertical cylinder of cross-sectional area A is fitted with a tight-fitting, frictionless piston of mass m (Fig. P18.40). The piston is not restricted in its motion in any way and is supported by the gas at pressure P below it. Atmospheric pressure is P0. We wish to find the height h in Figure P18.40. (a) What analysis model is appropriate to describe the piston? (b) Write an appropriate force equation for the piston from this analysis model in terms of P, P0, m, A, and g. (c) Suppose n moles of an ideal gas are in the cylinder at a temperature of T. Substitute for P in your answer to part (b) to find the height h of the piston above the bottom of the cylinder. Figure P18.40arrow_forwardReview. (a) Derive an expression for the buoyant force on a spherical balloon, submerged in water, as a function of the depth h below the surface, the volume Vi of the balloon at the surface, the pressure P0 at the surface, and the density w of the water. Assume the water temperature does not change with depth, (b) Does the bouyant force increase or decrease as the balloon is submerged? (c) At what depth is the buoyant force one-half the surface value?arrow_forward
- Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- College PhysicsPhysicsISBN:9781285737027Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningPhysics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning